Answers
Answer : (-∞,-1) U (-1, 1)
We need to find the interval(s) over which the function is increasing
We look at the intervals of x where the graph is increasing
Increasing interval of the graph is the part where the graph goes up.
At first the graph starts increasing and it increases till x=-1
So the first increasing interval is -infinity to -1 . We write it as (-∞,1)
Now, we look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph starts increasing at x=-1 and increases till it changes direction. The graph is increasing till x=1
so second increasing interval is x=-1 to 1. we write it as (-1,1)
Now combine both intervals by a 'U' union
(-∞,-1) U (-1, 1)
The interval(s) over which the function that is increasing is (-∞,-1) U (-1, 1)
What is the intervalFrom the question, One need to find the interval(s) over which the function is increasing
Since intervals of x where the graph is increasing Increasing interval of the graph is the part where the graph goes up.
At first the graph starts increasing and it increases till x=-1, So the first increasing interval is -infinity to -1 . We write it as (-∞,1). So, one look at the part where the graph changes direction
In the middle inverted U shaped graph , the graph starts increasing at x=-1 and increases till it changes direction. The graph is increasing till x=1
Since the increasing interval is x=-1 to 1. one then need to write it as (-1,1)
So, The function is increasing for all values of x in the open interval from negative infinity to negative 1, excluding -1, and also in the open interval from -1 to 1, excluding both -1 and 1."
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Related Questions
Please Help!
Multiply. −3/10xy(60xy^6) Enter your answer in the box.
Answers
Answer:
first we will multiply -3/10 and 60,
-3/10 x 60 = -18
(one-tenth of 60 is 6, and because we are multiplying -3/10 and not -1/10 we can multiply 6 by -3 to get 18.)
then multiply the exponents
x(x) = x^2
y(y^6) = y^7
we can then multiply all terms together to form one single term
-18(x^2)y^7=-18x^2y^7
our final answer is:
-18x^2y^7
The answer to the given question is [tex]\[ \boxed{-18x^2y^7} \][/tex]
First, we need to multiply the numerical coefficients and the literal coefficients (variables) separately. The numerical coefficients are -3 and 60, and the literal coefficients are 1/10, x, y, x, and [tex]y^6[/tex].
Multiplying the numerical coefficients:
[tex]\[ -3 \times 60 = -180 \][/tex]
Multiplying the literal coefficients (variables):
[tex]\[ \frac{1}{10} \times x \times y \times x \times y^6 \][/tex]
Since we have two x's and one y to the power of 6, we can simplify this as:
[tex]\[ \frac{1}{10} \times x^2 \times y^7 \][/tex]
Now, we combine the numerical and literal coefficients:
[tex]\[ -\frac{180}{10} \times x^2 \times y^7 \][/tex]
Simplifying the numerical fraction:
[tex]\[ -18 \times x^2 \times y^7 \][/tex]
Therefore, the final simplified expression is:
[tex]\[ -18x^2y^7 \][/tex]
The answer is: [tex]-18x^2y^7[/tex].
Solve the inequality. q + 12 – 2(q – 22) > 0
Answers
Step 1. Expand
q + 12 - 2q + 44 > 0
Step 2. Simplify q + 12 - 2q + 44 to -q + 56
-q + 56 > 0
Step 3. Regroup terms
56 - q > 0
Step 4. Subtract 56 from both sides
-q > -56
Step 5. Multiply both sides by -1
q < 56
To solve the inequality q + 12 – 2(q – 22) > 0, distribute the negative sign, isolate the variable, and divide by -1 with a flipped inequality sign to find q < 56.
Explanation:To solve the inequality q + 12 – 2(q – 22) > 0, we can start by distributing the negative sign to the terms inside the parentheses: q + 12 - 2q + 44 > 0. Simplifying, we have -q + 12 + 44 > 0, which becomes -q + 56 > 0. Next, we isolate the variable by subtracting 56 from both sides: -q > -56. Finally, we divide both sides by -1, remembering to flip the inequality sign when dividing by a negative number: q < 56.
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need help k=(-1)
d=(-2)
Answers
6 is your answer good luck
What is the difference of the polynomials? (m^2n^2-7)-(mn+4)
Answer choices
mn – 11
mn + 3
m^2n^2-mn-11
m^2n^2-mn-3
Answers
Answer: The difference is,
[tex]m^2n^2-mn-11[/tex]
Step-by-step explanation:
Given expression is,
[tex](m^2n^2-7)-(mn+4)[/tex]
By distributive property,
[tex]m^2n^2-7-mn-4[/tex]
Combine like terms( that have the same variables and powers ),
[tex]m^2n^2-mn-11[/tex]
Which is the required result.
Hence, option third is correct.
The graph shows Kelly traveling from home to her grandmother's house: A graph is shown with the title Kelly's drive. The x-axis is labeled Time driving, and the y-axis is labeled Distance driven. Segment A begins at the origin and continues quickly upward until x equals 0.5. Segment B is a horizontal line from x equals 0.5 until 1.75. Segment C moves in an upward direction until x equals 3. Segment D moves in an upward direction until x equals 3.5 Which interval on the graph indicates she is stuck in a traffic jam? A B C D
Answers
Answer:
The correct option is: B
Step-by-step explanation:
The x-axis is labeled Time driving, and the y-axis is labeled Distance driven.
Segment B is a horizontal line from x equals 0.5 until 1.75.
So, the value of [tex]y[/tex] is constant in the interval [tex]x=0.5[/tex] to [tex]x=1.75[/tex] is 0.
Thus, the distance traveled in the time interval 0.5 to 1.75 will be 0, which means the car was in the same position in that time interval.
So, the interval B on the graph indicates she is stuck in a traffic jam.
Answer:
B
Step-by-step explanation:
Cookies come in trays of 100 tovah needs 700 cookies she has 300 cookies
Answers
The question centers on mathematics, where we calculate the number of cookies Tovah needs and explore probability and trading scenarios related to assorted cookies and resource allocation.
Explanation:The subject of this question is Mathematics, particularly focusing on basic arithmetic, probability, and problem-solving. Tovah needs a total of 700 cookies and already has 300 cookies. To determine how many more cookies Tovah needs, we can subtract the number she already has from the total number needed: 700 - 300 = 400. Hence, she needs to obtain 400 more cookies.
Additionally, when discussing assorted cookies, we can delve into probability and combinatorics. For instance, if we consider a scenario with cookies containing chocolate, nuts, or both, we can calculate the probability that a certain combination is selected. This involves understanding percentages, probability trees, and independence of events.
Lastly, we can explore resource allocation and trading as seen in examples where individuals barter items like chocolate bars or Halloween candy. This introduces concepts like gains from trade and distribution of resources, which are essential to economic mathematics.
Geometry help? : which triangle could NOT be similar to triangle ABC ?
Answers
I think that the answer is the 4th triangle hope this helped.
That would be triangle DEF and the last one (M - -)
The corresponding sides compared with triangle ABC are not in same ratio
find an equation of a line containing the points (-6,1) and (2,-5).
Answers
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (2, - 5 )
m = [tex]\frac{-5-1}{2+6}[/tex] = [tex]\frac{-6}{8}[/tex] = - [tex]\frac{3}{4}[/tex]
the partial equation is
y = - [tex]\frac{3}{4}[/tex] x + c
to find c substitute either of the 2 given points into the partial equation
using (- 6, 1 ), then
1 = [tex]\frac{9}{2}[/tex] + c ⇒ c = 1 - [tex]\frac{9}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line
***HELP***
what does the "o" mean in geometry transformation notation?
for example: T(6,-1) o Rx-axis o r(180,0)
Answers
I think it's degrees or like something to do with translating?!
It is function composition. If you have one function f(x), and another function g(x), then we can create a new function named g∘f (read as: "gg composed with ff") that is defined as(g∘f)(x)=g(f(x))(g∘f)(x)=g(f(x))For example, if f(x)=x+1f(x)=x+1, and g(x)=2x−1g(x)=2x−1, then(g∘f)(x)=g(f(x))=g(x+1)=2(x+1)−1=2x+1
Naomi starts the engine on her small private airplane. The engine drives a propeller with a radius of 8 feet and its centerline 13 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 700 revolutions per minute. The height of one propeller tip as a function of time is given by h = 13 + 8 sin(700t), where h is the height in feet and t is the time in minutes. Use degrees to find h when t = 4 minutes.
Answers
Answer:
5.13 feet
Step-by-step explanation:
Engine is driving the propeller with a radius of 8 feet and its centerline 13 feet above the ground.
And the speed is 700 revolutions per minute, the height of one propeller tip as a function of time is given by:
[tex]h=13+8 \sin(700t)[/tex]
We have been asked to find the value of height, 'h', when t=4 minutes.
Plugging the value of time, 't', in the equation, we already know that we need to use degrees (not radians) we get:
[tex]h=13+8 \sin (700 \times 4)[/tex]
[tex]h=13+8 \sin (2800)[/tex]
[tex]h=13+8 \times (-0.984)[/tex]
[tex]h=13+(-7.872)[/tex]
[tex]h=13-7.872[/tex]
[tex]h=5.128\approx 5.13[/tex]
So the height of one propeller tip at t=4 minutes is 5.13 feet.
The basic equation for calculating compound interest is A=P(1+r/n)^(nt). If 1400 is inve if 1400 is inverested at an interest rate of 6% per year, compounded quarterly, how much will the investment be worth at the end of 10 years?
Answers
Answer:
2539.63
Step-by-step explanation:
A = 1400(1 + 0.06/4)^(4*10)
= 2539.63
your cell phone company started a rewards club. For every three text sent, you get 15 points. You need 1800 points for prize. How many tags do you need to send to get that prize?
Answers
You need to send 360 texts to earn 1800 points and get the prize.
To figure out how many texts you need to send to obtain the prize from your cell phone company's reward club, you'll want to set up a proportion because you earn a set number of points for every several texts sent. In this case, you get 15 points for every three texts.
Let's use the variable T to denote the total number of texts needed to be sent. We know that:
3 texts = 15 points
T texts = 1800 points
To find T, we can set up a ratio and solve for the variable:
[tex]\(\frac{3 texts}{15 points} = \frac{T texts}{1800 points}\)[/tex]
Cross multiply to solve for T:
3 texts * 1800 points = 15 points * T texts
T = [tex]\(\frac{3 * 1800}{15}\)[/tex]
T = 360 texts
Therefore, you need to send 360 texts to earn 1800 points and get the prize.
One month julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers.How much was the supply of rainwater increased or decreased by the end of the month
Answers
Given
One month julia collected 8.4 gallons of rainwater.
she used 5.2 gallons of rainwater to water her garden
6.5 gallons of rainwater to water flowers
Find out how much was the supply of rainwater increased or decreased by the end of the month.
To proof
As given in the question
One month julia collected 8.4 gallons of rainwater
she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers
Total water she used in the month = 5.2 gallons + 6.5gallons
= 11.7 gallons
Let the supply of rainwater increased or decreased by the end of the month
be x .
Than the equation become in the form
x + 8.4 = 11.7
x = 3.3 gallons
Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.
Hence proved
Total rainwater collected by Julia = 8.4 gallons
Water used for watering garden = 5.2 gallons
Water used for watering flowers = 6.5 gallons
Hence, total water used by Julia = [tex]5.2+6.5=11.7[/tex] gallons
11.7 gallons were used and only 8.4 gallons were collected , so supply of rainwater decreased by [tex]11.7-8.4=3.3[/tex] gallons
Drag each symbol and number to the correct location on the inequality. Not all symbols and numbers will be used.
Will brought a 144-ounce cooler filled with water to soccer practice. He used 16 ounces from the cooler to fill his water bottle. He then took out 16 plastic cups for his teammates and poured the same amount of water into each cup.
Find the number of ounces of water, x, that Will could have poured into each cup.
Answers
Answer:
x ≤ 8
Step-by-step explanation:
Will first used 16 of the 144 ounces for his own water bottle. This leaves 144-16 = 128 ounces.
Dividing that equally amount 16 plastic cups, each cup would have at most
128/16 = 8 ounces.
This means each one would have x ≤ 8 ounces.
The correct inequality is 8 > 6 .
To solve this problem, we need to figure out how many ounces of water Will could pour into each cup. He started with a cooler filled with 144 ounces of water.
Then, he took out 16 ounces for his own water bottle. So, he had 144 - 16 = 128 ounces left.
Since he poured the same amount of water into each of the 16 cups, we can divide the total remaining ounces by the number of cups to find out how many ounces each cup contains:
[tex]\[ \frac{128}{16} = 8 \][/tex]
So, Will could have poured 8 ounces of water into each cup.
Therefore, the correct inequality is:
8 > 6
Draw 3 rows with 2 counters in each row. Write a word problem to that can be acted out using these counters
Answers
3×2=6
Jon is selling tickets for the school talent show. On the 1st day, he sold 3 senior tickets and 12 child tickets for $195. On the 2nd day he sold 13 senior tickets for $299. Find the price of a senior citizen ticket.
Answers
Jon is selling tickets for the school talent show. On the 1st day, he sold 3 senior tickets and 12 child tickets for $195. On the 2nd day he sold 13 senior tickets for $299. Find the price of a senior citizen ticket.
Answer:$23Create a system of equations to help you solve this problem. The system of equations will look like: 3s + 12c = 195 and 13s = 299. The variable s represents the cost of senior tickets and the variable c represents the cost of children tickets.
[tex]\left \{ {{3s~+~12c~=~195} \atop {13s~=~299}} \right.[/tex]
Solve the second equation for the variable s as this is the easiest way to solve the problem. Solve the second equation for s by dividing both sides of the equation by 13 to isolate the variable s.
s = 23
Since the question was only asking for the price of a senior citizen ticket, you are technically done. The first equation was only put there to confuse you or allow you to check your work if you needed to. The price of a senior citizen ticket (variable s) is $23.
Becky purchased a home entertainment center set for $2254
Answers
This isn't even the full question
May has 1,473 and kay has -44 what is the diference
Answers
The difference would be:
1,517.
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
Answers
Answer:
42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Step-by-step explanation:
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.654
For finding the percent of the variation in one variable explained by the other variable, we just need to take square of the correlation coefficient.
Here, [tex]r=0.654[/tex]
So, [tex]r^2 = (0.654)^2 = 0.427716[/tex]
Now, for converting it into percentage, we will multiply it by 100.
So, [tex]0.427716*100\% = 42.7716 \%[/tex]
Thus, 42.7716% of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers.
Final answer:
About 42.8% of the variation in the bags of trash collected can be attributed to the number of volunteers, as indicated by the squared correlation coefficient (0.654²).
Explanation:
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. When squared to calculate the coefficient of determination (r²), it represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In the given scenario, with a correlation coefficient of 0.654, the coefficient of determination would be 0.654², which calculates to approximately 42.8%. This percentage indicates that about 42.8% of the variation in the number of bags of trash collected (y) can be explained by the variation in the number of volunteers (x).
A survey of teens showed that teens in brooklyn, ny aged 13-18 spend 16.9 hours per week online. Teens in charlotte, nc spend 13.2 hours per week online. Write and solve an addition equation to find the difference on time spent online by teens in these cities
Answers
To work this out we have to do 16.9 hours - 13.2 hours = 3.7 hours so there is a 13.7hour difference and to show it as an addition equation you do 13.2 hours + 3.7hours = 16.9 hours
The difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.
Explanation:To find the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC, we can write and solve an addition equation.
Let's define:
x = time spent by teens in Brooklyn, NY (in hours)y = time spent by teens in Charlotte, NC (in hours)The equation is: x + y = difference in time spent online
Given that teens in Brooklyn, NY spend 16.9 hours per week online and teens in Charlotte, NC spend 13.2 hours per week online, we can substitute these values into the equation:
16.9 + 13.2 = difference in time spent online
Simplifying the equation, we get:
difference in time spent online = 30.1 - 13.2
Therefore, the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.
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A sugar bowl holds 237 grams. You have a one kilogram bag of sugar. Estimate how many bowls of sugar you can fill from the bag.
Answers
Answer:
The required number of bowls are 5.
Step-by-step explanation:
Given : A sugar bowl holds 237 grams. You have a one kilogram bag of sugar.
To find : Estimate how many bowls of sugar you can fill from the bag?
Solution :
1 bowl can hold 237 gram of sugar.
We have, 1 kg of sugar or 1000 gram of sugar.
According to question,
237 gram of sugar can hold in 1 bowl.
So, 1 gram of sugar can hold in [tex]\frac{1}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]\frac{1000}{237}[/tex] bowl.
1000 gram of sugar can hold in [tex]4.21[/tex] bowl.
Which means, The required number of bowls are 5.
As 4 bowls have [tex]237\times 4=948[/tex] grams of sugar.
Sugar left is 1000-948=52 grams
That 52 grams is filled into 5th bowl.
PLS HELP! 20 PTS
Use rounding to determine if the answer is reasonable. Round each of the factors to the nearest ten, then multiply. 587 × 92 = 54,004
Answers
587 rounded to the nearest ten is 590, and 92 is 90. Then, take 590 times 90 to get 53100. The two answers are in the same ballpark, so yes, the answer is reasonable.
Examine this set of Pythagorean triples. Look for a pattern that is true for each triple regarding the difference between the three values that make up the triple.
Describe this pattern. Then see if you can think of another Pythagorean triple that doesn’t follow the pattern you just described and that can’t be generated using the identity (x2 − 1)2 + (2x)2 = (x2 + 1)2. Explain your findings.
I have attached an image of the triples. If anyone could help me with this, I'd greatly appreciate it. Please respond correctly. Tysm.
Answers
A Pythagorean triplet is a set of 3 positive integer numbers which may be the sides of a right triangle, i.e. they meet the Pythagorean theorem c² = a² + b².
You can check that the numbers on your table are Pythagorean triplets by substituting them in the Pythagorean equation:
6² + 8² = 36 + 64 = 100 = 10²8² + 15² = 64 + 225 = 289 = 17²10² + 24² = 100 + 576 = 676 = 26²12² + 35² = 144 + 1225 = 1369 = 37²
Now, lets look for the pattern:
x-value Pythagorean
triple
3 (6, 8, 10) 6/2 = 3
3² - 1 = 9 - 1 = 8
3² + 1 = 9 + 1 = 10
----------------------------------------------------------------------
4 (8, 15, 17) 8/2 = 4
4² - 1 = 16 - 1 = 15
4² + 1 = 16 + 1 = 17
---------------------------------------------------------------------
5 (10, 24, 26) 10/2 = 5
5² - 1 = 25 - 1 = 24
24² + 1 = 25 + 1 = 26
--------------------------------------------------------------------------
6 (12, 35, 37) 12/2 = 6
6² - 1 = 36 - 1 = 35
6² + 1 = 36 + 1 = 37
----------------------------------------------------------------------
From which you find the pattern: the first number is 2x, the second number is x² - 1, and the third number is x² + 1
⇒ (2x)² + (x² - 1)² = (x² + 1)², or
(x² - 1)² + (2x)² = (x² + 1)².
Other example of a Pythagorean triple is (3, 4, 5). You migth think that it does not follow the pattern, but if you do x = 2, you end with:
x = 22x = 2(2) = 4x² - 1 = 2² - 1 = 3x² + 1 = 2² + 1 = 5Hence, (3, 4, 5) also follows the pattern.
Only right triangles with non-integer sides do not form Pythagorean triples.
Of course you may proof that (x² - 1)² + (2x)² = (x² + 1)² is an identity (always true):
Left hand side: (x⁴ - 2x² + 1) + 4x² = x⁴ + 2x² + 1
Right hand side: x⁴ + 2x² + 1
∴ The equation is always true.
At the end, the pattern is true for any Pythagorean triplet, but a more formal proof is beyond the scope of this question.
Florence began deriving the quadratic formula. ax² + bx + c = 0 x2+bax+ca=0 x2+bax=−ca What step should Florence do next?
Answers
The solution to ax² + bx + c = 0 is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
What is a quadratic function?A quadratic function is an equation of degree 2.
Given the equation:
ax² + bx + c = 0
Subtracting c from both sides to get:
ax² + bx = -c
Dividing through by a:
x² + (b/a)x = -c/a
Add to both sides the square of half of the coefficient of x that is (b²/4a):
x² + (b/a)x + (b²/4a)= -c/a + (b²/4a)
(x + b/2a)² = (b²-4c/4a)
[tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
The solution to ax² + bx + c = 0 is [tex]x=-\frac{b}{2a}\pm\sqrt{\frac{b^2-4c}{4a} }[/tex]
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Final answer:
Next, Florence should complete the square on the quadratic equation by dividing by 'a' (if applicable), moving the constant term to the other side, and adding the square of half the coefficient of 'b' to both sides. This is a precursor step toward factoring and ultimately deriving the quadratic formula.
Explanation:
The step Florence should do next in deriving the quadratic formula from the equation ax² + bx + c = 0 is to complete the square. To do this, Florence first needs to divide the entire equation by a to normalize the coefficient of x² to 1, assuming a≠0. Then she should move the constant term to the other side of the equation to get x² + (b/a)x = -c/a. The next step is to add the square of half of the coefficient of x to both sides of the equation, which is (b/2a)². This process sets the stage for factoring the left side of the equation as a perfect square.
Once the perfect square is created, the equation can be written in the form (x + b/2a)² = (b² - 4ac)/4a². Then, by taking the square root of both sides and isolating x, Florence will arrive at the quadratic formula: x equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c’, all over two 'a'.
Use the equation y=7x+3 to determine the ordered pairs when x=2 and x=-1
please help ☹️
Answers
I already learned this so I think this is the answer
Carmela mixes 3/4 kilogram of walnuts, 1/2 kilogram of almonds, and 1/4 kilogram of pecans together. She divides the mixed nuts into 3/10 kilogram bags. How many bags of mixed nuts does she have.
Answers
Answer:
5
Step-by-step explanation:
The total number of bags of mixed nuts with Carmela are 5.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Carmela who mixes 3/4 kilogram of walnuts, 1/2 kilogram of almonds, and 1/4 kilogram of pecans together. She divides the mixed nuts into 3/10 kilogram bags.
We can write the equation as -
(3/4 + 1/2 + 1/4) x 1000 = (3/10) x 1000 x n
1.5 x 1000 = 3 x 100 x n
1.5 x 10 = 3n
15 = 3n
n = 5
Therefore, the total number of bags of mixed nuts with Carmela are 5.
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There were 5 girls and 22 boys in math express the number of girls as a fraction of the number of boys then express the fraction as a decimal
Answers
5/22 is the fraction of girls to boys and as a decimal it is 2.3 rounded and not rounded is 2.27 repeated.
If michael family has 210 acres and each cow take 1/3 acre of grazing how many cattle could their farmland support
Answers
210÷1/3
=210×3
=630
Therefore, the farmland could support 630 cattles.
Hope it helps!
Michael drove 350 miles in 7 hours at a constant speed. Is the unit rate for miles to hours 50?
Answers
Answer:
Unit rate of driving (speed) is 50 miles per hour
Step-by-step explanation:
Michael drove 350 miles in 7hrs
Speed = Distance ÷ time
Speed= 350 miles ÷ 7 hours = 50 miles per hour.
Amerada Hess company wants to make an oil container tank. Engineers are shown a sample tank. which is 1 meter in height, and they are told that the new tank should look similar to the sample. If the sample tank is 1/25 the size of the original tank. what is the height of the original tank?
A. 25m
B. 20m
C. 10m
D. 1m
Answers
[tex]1 = \frac{1}{25} x[/tex]
x is the height of our container. we need to move 1/25 to the other side so we multiply both sides of the equation by 25.
[tex]25 \times 1 = \frac{1}{25} x \times 25[/tex]
On the right side of the equation, 1/25 cancels out with 25 since:
[tex] \frac{1}{25} \times 25 = 1[/tex]
so we are left with the 25 x 1 on the left:
[tex]25 = x[/tex]
so the container is 25m; C.
To find the height of the original oil tank from the sample, you set up a proportion using the scale given. The calculation shows that the original tank is 25 meters tall, corresponding to answer A.
The question is asking us to find the height of the original oil tank given that the sample tank is [tex]\frac{1}{25}th[/tex] the size of the original and that the sample is 1 meter tall. Since the sample is a scaled-down version of the original, we can set up a proportion to find the original height.
To set up the proportion, we assume the scale is such that 1 meter on the sample represents 25 meters on the original. Therefore, we can write the proportion as:
[tex]\frac{1\ meter}{ x\ meters} = \frac{1}{25}[/tex]
We can then cross-multiply to solve for x:
1 * x = 25 * 1
x = 25 meters
Thus, the height of the original oil container tank is 25 meters, which corresponds to answer choice A.